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Jun 24, 2016 - ABSTRACT: We report Stark fluorescence spectroscopy investigation of rubrene dispersed in a poly(methyl methacrylate) film. The feature...
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Stark Spectroscopy of Rubrene. II. Stark Fluorescence Spectroscopy and Fluorescence Quenching Induced by an External Electric Field Toshifumi Iimori,*,† Ryuichi Ito,† and Nobuhiro Ohta‡ †

Department of Applied Chemistry, Muroran Institute of Technology, Muroran 050-8585, Japan Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, 1001 Ta-Hsueh Rd., Hsinchu 30010, Taiwan

‡

S Supporting Information *

ABSTRACT: We report Stark fluorescence spectroscopy investigation of rubrene dispersed in a poly(methyl methacrylate) film. The features of the fluorescence spectrum are analogous to those in solutions. In the Stark fluorescence spectrum, the decrease of the fluorescence quantum yield in the presence of an external electric field is observed. This result shows that the yield of nonradiative decay processes is increased by the application of an external electric field. It is known that the fluorescence quantum yield for rubrene, which is nearly unity at room temperature, depends on temperature, and a major nonradiative decay process in photoexcited rubrene is ascribed to a thermally activated intersystem crossing (ISC). Equations that express the field-induced fluorescence quenching in terms of the molecular parameters are derived from the ensemble average of electric field effects on the activation energy of the reaction rate constant in random orientation systems. The molecular parameters are then extracted from the observed data. It is inferred that the field-induced increase in the yield of other intramolecular and intermolecular photophysical processes in addition to the ISC should be taken into account. presence and absence of an external electric field is measured. SF spectroscopy enables photophysics and photochemistry of molecules and the mechanism of the electric field effects on them to be understood.12 The fluorescence quantum yield depends on both the radiative and nonradiative decay rates. If these decay processes are affected by the application of an external electric field, then the change in the fluorescence quantum yield can be measured in addition to the Stark effect on the fluorescence bands by using SF spectroscopy. Because the nonradiative decay processes include the ISC to the triplet states and singlet fission, SF spectroscopy is potentially useful to obtain information on the change in the photophysics in the presence of an external electric field.

I. INTRODUCTION A major relaxation process from the photoexcited state of rubrene is fluorescence, and the fluorescence quantum yield is nearly unity in solutions and solid matrices including polymers and organic glasses. Although the yield of nonradiative decay processes is small, the intersystem crossing (ISC) to a triplet state occurs with a yield of ca. 0.01.1 In single crystals of rubrene and amorphous rubrene films, singlet fission, in which two triplet excitons are generated from one singlet exciton, has been observed.2−8 The singlet fission in molecular solids is under active investigation because this can lead to the increase in the efficiency of photovoltaic cell beyond the theoretical limit in conventional single-junction photovoltaic cells.8,9 Bright fluorescence of rubrene is also useful for the application to organic light emitting devices (OLED), and in fact, rubrene has been used as an emitting dopant molecule in OLED.4,10 In OLED devices, molecules in thin films are subjected to high electric fields. However, the effect of an external electric field on the photophysical processes including the ISC and the emission in OLED devices remains open question. In a series of papers (i.e., Part I11 and this paper, which is Part II), we report Stark spectroscopy investigation of rubrene dispersed in a polymer matrix. In the companion paper (Part I), we reported the results of electroabsorption (EA) spectroscopy or Stark absorption spectroscopy, and the molecular parameters including the polarizability difference between the excited and ground states were determined. Here, as Part II, we report electro-photoluminescence spectroscopy or Stark fluorescence (SF) spectroscopy investigation, in which the difference spectrum between the fluorescence spectra observed in the © 2016 American Chemical Society

II. EXPERIMENTAL METHODS The method of sample preparation has already been described in Part I.11 The sample substrate has the layered structure of quartz/ITO/(rubrene/PMMA)/aluminum, where ITO denotes the indium tin oxide film, and rubrene/PMMA represents a poly(methyl methacrylate) film in which rubrene is dispersed. The sample was prepared by using spin-coating technique, and the benzene solution containing ∼3% by mass PMMA and ∼3 mM rubrene was used, unless otherwise noted. The molar ratio of rubrene to PMMA monomer unit was then 1 mol %. The sample substrate was placed in vacuum by using a vacuum chamber having quartz windows, unless otherwise noted. The Received: March 14, 2016 Revised: June 22, 2016 Published: June 24, 2016 5497

DOI: 10.1021/acs.jpca.6b02627 J. Phys. Chem. A 2016, 120, 5497−5503

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The Journal of Physical Chemistry A chamber was evacuated to a pressure below 1 × 10−3 Pa prior to measurements. The actual concentration of rubrene should be slightly lower than 1 mol % due to the evaporation of rubrene in vacuum. In SF spectroscopy, which measures the change in fluorescence intensity induced by the application of an external electric field as a function of fluorescence wavelength, a spectrofluorometer (FP-777, JASCO) was used as a base instrument.12 An unpolarized monochromatic light from a Xe lamp was used as an excitation light, and unpolarized fluorescence was monitored by using a photomultiplier tube through a monochromator. The alternating current (AC) voltage having a frequency of 40 Hz was applied to the rubrene/PMMA film. The signal from the photomultiplier tube comprised direct current and modulated components. They were detected by using an analog-to-digital converter and a lock-in amplifier (Stanford Research Systems) at the second harmonic of the frequency of the applied AC voltage, respectively. In SF measurement, we checked the fluorescence spectra before and after each wavelength scan. These fluorescence spectra were identical to each other, and accordingly we concluded that a fluorescence quenching caused by photochemical reaction or photo-oxidization in the measurement could be neglected. Fitting of SF and fluorescence spectra was performed by using the IGOR program (Wavemetrics).

absorption occur between the S1 and S0 electronic states of rubrene. Thus, we can assume the molecular parameters such as Δα̅ to be nearly identical between the electronic transitions for absorption and fluorescence. Moreover, we can assume that the molecules are immobilized in PMMA and that the reorientation in the presence of F is negligible for nonpolar molecules such as rubrene. From the result of the EA spectroscopy investigation, we can approximately write the coefficient Bφ′ as11

Bφ′ =

IV. RESULTS IV.A. Fluorescence and Absorption Spectra. As shown by the singlet fission and delayed fluorescence in single crystals, the presence of intermolecular interaction due to the formation of aggregates or microcrystals may result in the photophysics different from that for the isolated rubrene. It is important to inspect the possibility of such intermolecular photophysical processes to discuss the results of the SF spectroscopy. If the formation of molecular aggregates or microparticles in PMMA is negligible, the absorption and fluorescence spectra should resemble those in dilute solution. In Figure 1, we compare the absorption and fluorescence spectra for the toluene solution containing ∼1 × 10−5 M rubrene with those for the rubrene/ PMMA film containing 1 mol % rubrene. The spectra for the rubrene/PMMA film containing rubrene at a lower concentration (0.2 mol %) are also shown. All of the spectra in Figure 1 were measured in air. The 0.2 mol % rubrene/PMMA film was prepared by using the benzene solution containing ∼10% by mass PMMA and ∼0.7 mM rubrene. In a polymer film containing polystyrene and rubrene at the same concentrations with this film, respectively, the rubrene molecule is known to be dispersed in isolated condition.2 The observed fluorescence lifetime (∼16 ns) was close to the natural radiative lifetime, and this result shows that the fluorescence quantum yield is close to unity and that the presence of intermolecular photophysical processes is negligible.2 Although the polymers used in the fluorescence lifetime measurement and in this work are

⎡ d ⎧ I (ν) ⎫ d2 ⎧ I (ν) ⎫⎤ ΔIFL(ν) = (fF ) ⎢Aφ′ IFL(ν) + Bφ′ ν 3 ⎨ FL 3 ⎬ + Cφ′ ν 3 2 ⎨ FL 3 ⎬⎥ dν ⎩ ν ⎭ d ν ⎩ ν ⎭⎦ ⎣ 2

(1)

where ν is the frequency, f is the internal field factor, F is the electric field externally applied to the film, F = |F|, IFL(ν) is the unperturbed fluorescence spectrum, φ is the angle between F and the electric vector of the fluorescence, which is experimentally determined by a polarizer in the fluorescence path, and the coefficients Aφ′ , Bφ′ , and Cφ′ respectively represent the contribution of the zeroth, first, and second derivatives of the fluorescence spectrum divided by ν3. The first and second derivative components arise from the shift and broadening of the fluorescence spectrum.12 We used unpolarized light for both the photoexcitation and fluorescence, and accordingly the angle φ cannot be determined experimentally. However, we can determine a few molecular parameters from the experiments using unpolarized light. The coefficient B′φ is given by an expression that is similar to eq 4 in Part I for the EA spectrum,11 and it is related to the difference in the polarizability: 1 Tr(αfl − αg) 3

(3)

The coefficient Cφ′ is a function of the difference Δμ = |Δμ| = |μfl − μg|, where μfl and μg are the dipole moments for the fluorescent state and the FC ground state, respectively.11 The explicit form of the coefficient C′φ is given by eq 5 in Part I with the replacement of the angle χ with φ.11 The zeroth derivative component Aφ′ corresponds to the field-induced change in fluorescence intensity. If molecules are immobilized and the change in absorbance induced by F is negligible at the wavelength of photoexcitation, the coefficient Aφ′ should originate from the field-induced change in fluorescence quantum yield and the field-induced change in transition dipole moment.11 Both of these contributions are independent of the angle φ, and thus the discussion of them in the SF spectroscopy using unpolarized light is rationalized. The fieldinduced change in the fluorescence quantum yield can be ascribed either to the field effects on radiative and/or nonradiative rate constants or to the field-induced change in the population of the fluorescent state. Thus, one can understand the electric field effects on photoexcitation dynamics from the zeroth derivative component. In this work, the reported parameters and calculations are not corrected for the internal field factor f, and it is assumed to be unity. The details on the correction for the f has been reported in Part I.11

III. THEORETICAL BACKGROUND Although a theory of SF spectroscopy is analogous to that of EA spectroscopy, there is a difference in the molecular parameters that can be determined. Whereas the EA spectrum stems from the difference in molecular parameters between the Franck−Condon (FC) excited state and the ground state, the SF spectrum is related to the difference in the molecular parameters between the fluorescent state and the FC ground state. The SF spectrum [ΔIFL(ν)] can be written as12,13

Δα̅ =

Δα̅ 2h

(2)

where αfl and αg denote the polarizability tensors for the fluorescent state and the FC ground state, respectively. The electronic transitions both for the fluorescence and for the 5498

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quantum yields for different samples by calculating the fluorescence intensity divided by the absorbance of the sample under the same experimental condition. If microparticles are present and the singlet fission occurs in the 1 mol % rubrene/ PMMA film, we can expect that the fluorescence quantum yield for the 1 mol % film is smaller than that for the 0.2 mol % film. By using this steady-state method, we tentatively compared the relative fluorescence quantum yields for the rubrene/PMMA films containing 1 and 0.2 mol % rubrene. The 1 mol % film seemingly showed a small decrease of the fluorescence quantum yield in comparison with the 0.2 mol % film. However, a quantitative discussion was hampered by unexpected variation in the fluorescence intensity at different positions on a single rubrene/PMMA film. Despite the limited accuracy of the method, it is likely that the variation of the fluorescence quantum yields for the two films is much smaller than that which is expected between the isolated molecule and the microparticles showing the singlet fission. Therefore, we believe that the contribution of the singlet fission or other intermolecular photophysical processes due to the formation of aggregates or microparticles must be minor in our measurements, although it may exist. Future measurements of the fluorescence lifetime by using time-resolved spectroscopy and the fluorescence quantum yield will bring a more definite characterization of our samples. In solutions or isolated condition, the most stable structure of rubrene has a twisted tetracene backbone (Figure 2c in Part I).11 Thus, we can assume the twisted structure for rubrene isolated in a PMMA matrix. In the fluorescence spectrum, the direction of the transition moment m for the dominant band system is parallel to the short axis of the tetracene backbone and the same as the absorption.14 In single crystals, much weaker bands for which polarization directions are different from those for the dominant band system are also observed due to vibronic interaction with other electronic states.14 IV.B. Stark Fluorescence Spectrum. Fluorescence spectrum excited at 468 nm and the result of the curve fitting by using a sum of Gaussian line shapes are shown in Figure 2a. The fluorescence maximum was observed at ∼17 900 cm−1 (558 nm). The center wavenumbers of the Gaussian line shapes for the three vibronic progressions are 1.80 × 104, 1.68 × 104, and 1.56 × 104 cm−1. The frequency of the progression is thus ca. 1.15 × 103 cm−1. In the photoluminescence spectrum for single crystals of rubrene, a progression having the frequency of 1.18 × 103 cm−1 appears,14 and this is similar to that observed in the rubrene/PMMA film. The SF spectrum measured at the field strength of 1.4 MV cm−1 and the excitation wavelength of 468 nm is shown in Figure 2b. In the SF spectrum, the negative signal appears in the wavenumber region higher than ∼16 500 cm−1, and its intensity is dominating over the small positive signal appearing at the lower wavenumber region. This feature indicates that the zeroth derivative component exists in the SF spectrum, and the negative sign represents the decrease of fluorescence intensity in the presence of an external electric field. The minimum of the SF spectrum appears at a slightly higher wavenumber than the fluorescence maximum. This shift indicates that there is a contribution from the first derivative component representing the field-induced redshift of the fluorescence spectrum in addition to the zeroth derivative component. The decomposed spectra of the fitting curve for the SF spectrum are shown in Figure 2c. The first- and second-

Figure 1. Normalized (a) absorption and (b) fluorescence spectra for the toluene solution and the rubrene/PMMA films containing 0.2 mol % and 1 mol % rubrene. The left and right axes show the intensities of the spectra for the toluene solution and the rubrene/PMMA films, respectively.

different from each other, it is reasonable to expect that the rubrene molecule in the 0.2 mol % rubrene/PMMA film is also isolated. The band positions and the bandwidths in the three absorption spectra are nearly identical to each other. The similarity of the spectra for the rubrene/PMMA films to those for the solution is consistent with the expectation that the rubrene molecule is isolated and does not form aggregates or microparticles. In addition, the similarity of the spectra suggests that the isolated rubrene gives rise to the same EA spectrum that the aggregates or microparticles should show, even if there exist aggregates or microparticles in PMMA. This result would advocate the interpretation of the EA spectra presented in Part I.11 The three fluorescence spectra are also similar to each other, although the rubrene/PMMA film containing 0.2 mol % rubrene shows a slight blueshift. The absorption and emission spectra for single crystals and an amorphous film of rubrene have been reported by Irkhin et al.14 They obtained the intrinsic spectra by eliminating experimental artifacts such as reabsorption effect. The intrinsic spectra in solution and of single crystals are very similar to each other. It has also been suggested that the variation of the fluorescence spectra for different systems including nanoparticles and microcrystals is not likely to be caused by size effects or morphology of the particles but may originate from experimental artifacts. The reason for the blueshift in the fluorescence spectrum for the 0.2 mol % rubrene/PMMA film (Figure 1) is not clear at present, but reabsorption effect caused by the overlap of the absorption and fluorescence spectra might explain the observation. If intermolecular photophysical processes such as the singlet fission occur in PMMA, the direct evidence of the occurrence can be given by the measurements of the fluorescence lifetime and fluorescence quantum yield. For example, in amorphous films, the fluorescence decay with the lifetime of ∼200 ps was assigned to the singlet fission, and 90% of the population of the excited singlet state undergo the singlet fission.2 In single crystals, the formation of the triplet state takes place on 5−50 ps time scales.3 The fluorescence quantum yields for these systems must become much smaller than unity. In steady-state spectroscopy, we can relatively compare the fluorescence 5499

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Table 1. Parameters Determined from the Fitting of Stark Fluorescence Spectrum of Rubrene parameters

valuesa

Δα̅ Aφ′ b

83 ± 6 Å (−2.3 ± 0.1) × 10−19 m2 V−2 3

a The reported values are not corrected for the internal field factor f. See the companion paper (Part I) about the correction for f.11 bA′φ is the coefficient for the zeroth derivative component that represents the field-induced change in the fluorescence quantum yield.

neglect the dependence on the parameter φ, we can obtain a similar Δμ with that obtained from the EA spectrum.11 The negative amplitude of the zeroth derivative contribution indicates that the application of an external electric field induces the decrease of the fluorescence quantum yield, namely, fluorescence quenching. In accord with the expectation from the first term (f F)2 A′φIFL (ν) in the right-hand side of eq 1, the amplitude of the zeroth derivative contribution showed the quadratic dependence on the field strength F (Figure 3). The

Figure 2. (a) Fluorescence spectrum (black line) measured with 468 nm excitation and the result of fitting (red line) with a sum of Gaussian line shapes (broken lines). (b) SF spectrum (black line) measured with 468 nm excitation and the field strength of 1.4 MV cm−1. (c) Contributions of the zeroth (dash-dot line), first (solid line), and second derivative (broken line) components in the fitting curve (red line in (b)) of the SF spectrum.

Figure 3. Plot of the contribution of the zeroth derivative component (|F|2 Aφ′ ) as a function of the square of the field strength (|F|2). The data for two independent experiments using different samples (sample1 and sample2) are shown. The broken line is a guide to show the linear dependence.

derivative line shapes were calculated from the whole fluorescence spectrum constructed by a sum of the Gaussian line shapes. The corresponding coefficients Bφ′ and Cφ′ were used as the fitting parameters. In the fitting process, the contribution of the zeroth derivative component was fixed to a value of the integral intensity of the SF spectrum divided by the integral intensity of the fluorescence spectrum over the whole wavenumber region. This is because the first- and secondderivative contributions should cancel and become zero after the integration over the whole wavenumber region of the fluorescence band. The fitting of the SF spectrum could be reasonably performed by using only a single set of the three coefficients. In the fluorescence spectrum, the emitting state is the S1 state, and the major electronic states, which are associated with the transition, are identical with those in the absorption spectrum. Therefore, following the discussion of the EA spectrum described in Part I,11 we can assume that the firstderivative coefficient Bφ′ in the SF spectrum is given by eq 3, as discussed in Section III. In this case, the dependence of Bφ′ on the angle φ is neglected. Thus, the experimental data, despite unpolarized fluorescence experiment, can afford to yield a physically meaningful result. The fitting parameter results in Δα̅ = 83 ± 6 Å3 (Table 1), which is in good agreement with the Δα̅ determined from the EA spectrum.11 The second-derivative component also appears in the SF spectrum. Under the unpolarized measurements in this work, accurate determination of the parameter of Δμ is difficult. If we

value of Aφ′ extracted from the data is shown in Table 1. This value corresponds to the efficiency of the field-induced fluorescence quenching. We obtain ΔΦF(F)/ΦF ≅ − 0.0023 at the field strength of 1 MVcm−1, where ΔΦF(F) and ΦF are the field-induced change in the fluorescence quantum yield and the fluorescence quantum yield in the absence of an external electric field, respectively. At the excitation wavelength of 468 nm (2.14 × 104 cm−1), the absorbance change (ΔA) induced by the application of the external electric field was negligibly small (Figure 3 in Part I).11 In fact, the value of ΔA at this excitation wavelength was smaller than 3 × 10−6 at F = 1 MV cm−1. However, the absolute value of ΔΦF(F)/ΦF is 2.3 × 10−3 at the same field strength. This fact shows that the contribution of the field-induced change in absorbance is not a dominant factor in the observed field-induced change in the fluorescence quantum yield. The field-induced fluorescence quenching has its origin in the change of the photophysical and/or photochemical processes induced by an external electric field. If the change in the radiative decay rate (kR) and/or the nonradiative decay rate (kNR) is induced by electric fields, then the fluorescence quantum yield also changes. Thus, the fieldinduced fluorescence quenching may be ascribed to the change in the radiative and/or nonradiative decay rate(s). The change in the population of the fluorescent state is probably negligible because of the ensuing reasons. First, the absorbance change induced by an external electric field is negligibly small at the 5500

DOI: 10.1021/acs.jpca.6b02627 J. Phys. Chem. A 2016, 120, 5497−5503

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The Journal of Physical Chemistry A excitation wavelength of 468 nm, that is, 21 400 cm−1.11 Second, differences in molecular geometries and electronic states between the FC excited state and the fluorescent state are expected to be very small, because both the absorption and fluorescence bands are assigned to the identical electronic transition. This expectation is experimentally underpinned by the observation that the values of Δα̅ determined from the EA and SF spectra were in agreement with each other. Therefore, electric field effects on the relaxation process from the FC excited state to the fluorescent state are hardly considered to be significant. As shown in Supporting Information, if the change in the radiative decay rate kR contributes to the change in the fluorescence quantum yield, its magnitude is approximately given by ΔkR (F) ΔΦF(F) ≈ (1 − ΦF) ΦF kR

spectrum are assigned to the single electronic transition for which the transition dipole moment lies parallel to the M-axis (Figure 2 in Part I),11 and the contribution of other transitions that have different polarization characters is negligible. While rubrene displays the high fluorescence quantum yield ΦF of nearly unity in solutions or organic matrices, it has been found that ΦF varies with temperature.16 A major nonradiative process in the isolated rubrene molecule was identified to be a thermally activated ISC to the T2 state.1 By assuming the Arrhenius equation for the temperature dependence of the rate of the S1 → T2 ISC, Löhmannsröben and co-workers have determined the activation energy (Ea) to be 860 cm−1 (0.11 eV).1 As the mechanism of the observed field-induced fluorescence quenching, it is straightforward to assume the field-induced change in the rate of the ISC, which is the major nonradiative process. In the presence of an external electric field, the energy levels for the T2 and S1 states that are associated with the ISC can be shifted due to the Stark effect (Figure 4). This energy-

(4)

where ΔkR(F) is the field-induced change in kR. The radiative decay rate kR is identical to the natural radiative decay rate and further is related to the molar absorption coefficient of the corresponding transition.15 Accordingly, we can evaluate ΔkR(F) from the field-induced change in the transition dipole moment. This effect can be evaluated from the zeroth derivative component observed in the EA spectrum.11 In fact, as described in Supporting Information, we have ΔΦF(F) = (fF )2 A χ (1 − ΦF) ΦF

Figure 4. Schematic illustration of the origin of the change in the ISC rate in the presence of an external electric field (F). In the absence of F, the thermally activated ISC from the S1 state to the T2 state occurs with the activation energy of Ea(F = 0) (black arrow). The interaction with F results in the Stark shift of the energy levels for these electronic states (bold red arrows). A resultant change in the activation energy [ΔEa(F)] is given by Ea(F) − Ea(F = 0), where Ea(F) represents the activation energy in the presence of F.

(5)

where Aχ is the coefficient for the zeroth derivative component in the EA spectrum. By using ΦF = 0.99 and the Aχ that is experimentally determined in Part I,1,11 ΔΦF(F)/ΦF ≅ − 4 × 10−6 is predicted at F = 1 MV cm−1. This value is much smaller than the experimental observation of ΔΦF(F)/ΦF ≅ − 2 × 10−3. Thus, we conclude that the contribution of the ΔkR(F), or the field-induced change in the transition dipole moment, cannot account for the observed field-induced fluorescence quenching. The fluorescence quenching caused by the change in the nonradiative decay rate (ΔkNR(F)) can be written by ΔΦF(F) = −ΔkNR (F)τ ΦF

level shift leads to the change in Ea, and the ISC rate is also expected to be affected. As shown in Supporting Information, the relation between the field-induced change [ΔEa(F)] in Ea and ΔΦF(F) is given by ⎛ ΔΦF(F) ⎞ 1 ⎛ ΔE (F) ⎞ exp⎜ − a ⎟ ⎟=1−⎜ ⎝ RT ⎠ ⎝ ΦF ⎠ 1 − ΦF

(6)

where τ is the fluorescence lifetime in the absence of an external electric field. The derivation of this relation is described in Supporting Information. From τ = 16 ns for the isolated rubrene in polystyrene2 and the experimentally observed ΔΦF(F)/ΦF (Table 1), we obtain ΔkNR(F) ≅ 1 × 105 s−1 at F = 1 MV cm−1. If τ is shorter than 16 ns in a rubrene/PMMA film, the calculated value of ΔkNR(F) becomes larger. In our experiments, the contribution of the intermolecular photophysical processes is likely to be minor, and the nonradiative decay rate should be mainly related to intramolecular photophysical processes. The mechanism of the field effects on intramolecular photophysical processes that give rise to the ΔkNR will be discussed in Section V.

(7)

where R is gas constant, and T is temperature. ΔEa(F) caused by the Stark shift is written as12,17 1 ΔEa(F) = −Δμ·F − F ·Δα ·F 2 F2 ∑ ΦFiΔαijΦFj = −F Δμcos θFΔμ − 2 ij (8) where Δμ and Δα represent the dipole moment and polarizability differences between the T2 and S1 states, respectively, θFΔμ is the angle made by the vectors Δμ and F, i and j represent the molecule fixed axes, ΦFi and ΦFj are the direction cosines between F and the molecule fixed axes, and Δαij is the component of Δα. As shown in the expression, Δμ and Δα are a vector and a tensor, respectively, and ΔEa(F) depends on the angles among the molecule fixed axes and the direction of an external electric field F.

V. DISCUSSION The SF spectrum was fitted by using a single set of the coefficients Aφ′ , Bφ′ , and Cφ′ without band separation. This result demonstrates that both the fluorescence spectrum and the SF 5501

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The Journal of Physical Chemistry A We can assume that molecules in PMMA films are immobilized and have random orientation. Under this assumption, we now calculate the average of the exponential function in eq 7 over all orientations of the molecules. Substitution of eq 8 in the left-hand side of eq 7 and the subsequent expansion of the exponential function up to second order for F result in17 ⎛ ΔE (F) ⎞ (F Δμ)2 2 F Δμ exp⎜ − a cos θFΔμ + cos θFΔμ ⎟≅1+ ⎝ RT ⎠ RT 2(RT )2 +

F2 2RT

Figure 5. Tentative values of the polarizability difference (Δα̅ ) and the dipole moment difference (|Δμ|) that can reproduce the observed magnitude of the field-induced change in the fluorescence quantum yield.

∑ ΦFiΔαijΦFj ij

(9)

We now use brackets to represent the rotational average over all orientations of the molecule fixed axes with respect to the direction of F:17 ⟨cos θFΔμ⟩ = 0

⟨ΦFiΦFj⟩ =

(10)

1 3

(11)

1 δij 3

(12)

⟨cos2 θFΔμ⟩ =

molecule such as rubrene. The physically unacceptable values of Δμ and Δα̅ might be understood by considering that a couple of nonradiative processes in addition to the ISC are concurrently affected by an external electric field, and we observed a sum of these individual contributions. It has been pointed out that the contribution of S1 → S0 internal conversion (IC) cannot be neglected at temperatures higher than room temperature to consistently explain the temperature dependence of the fluorescence intensity.1 Thus, it is possible that the enhancement of the IC rate in an external electric field also contributes to the observed field-induced fluorescence quenching. We considered that the contribution of the nonradiative processes due to the intermolecular interaction is minor. However, the photophysical processes between the rubrene molecules including the singlet fission might also become faster in the presence of an external field, if the molecular aggregates or microparticles exist in a rubrene/ PMMA film. The result of the SF spectroscopy investigation is consistent with the possibility that the rates of the intermolecular photophysical processes including the singlet fission are increased in the presence of an external field. For more understanding of the electric field effects on the photophysical process, a time-resolved measurement to directly determine the field-induced change in fluorescence lifetime is useful.18 Moreover, transient absorption spectroscopy, which detects the triplet state produced after the ISC or the singlet fission, can give valuable information if the comparison in the presence and absence of an external electric field can be made. If these processes make major contributions to the increase in the nonradiative decay rate in the presence of an external electric field, one can expect the resultant increase of the yield of the triplet state.

where δij is the Kronecker delta symbol. We then obtain ⎛ ΔE (F) ⎞ exp⎜ − a ⎟ ⎝ RT ⎠

≅1+

(F Δμ)2 F2 + Δα̅ 2RT 6(RT )2

(13)

The second and third terms in the right-hand side of this equation depend on F2. Thus, by combining eq 13 with eq 7, the field-induced quenching ΔΦF(F) is expected to have a quadratic dependence on F: −

⎤ ΔΦF(F) F 2 ⎡ (Δμ)2 1 = + Δα̅ ⎥ ⎢ RT ⎣ 6RT 2 ΦF(1 − ΦF) ⎦

(14)

This expectation is consistent with the experimental result (Figure 3). Therefore, the approximation using the expansion of the exponential function up to second order for F is validated. By solving eq 14, we can find Δμ and Δα̅, which can reproduce the experimentally observed ΔΦF(F). It is necessary to note that this calculation depends on the accuracy of the magnitude of (1 − ΦF)−1 that appears in the left-hand side of eq 14. The magnitude of ΦF is very close to unity, and accordingly the magnitude of 1 − ΦF becomes considerably small. We then must consider that the value of (1 − ΦF)−1 potentially contains significant error. Notwithstanding this uncertainty, we can tentatively calculate Δμ and Δα̅ that can satisfy eq 14 under ΔΦF(F)/ΦF = −2.3 × 10−3 observed at F = 1 MV cm−1, 1 − ΦF = 0.01,1 and T = 294 K. A set of Δμ and Δα̅ that can satisfy eq 14 is plotted in Figure 5. For example, in the extreme of Δα̅ = 0, we can see that a tentative value of Δμ must be 14 D. In contrast, in the extreme of Δμ = 0, a tentative value of Δα̅ must be 1.7 × 103 Å3. It is allowed for Δα̅ to be negative, and Δμ must increase with the decrease of Δα̅. Although the values of Δα̅ can be more negative than the lower limit in Figure 5, we show the plot for only the Δα̅ between −1.7 × 103 and 1.7 × 103 in units of cubic angstroms. This estimation contains error mainly due to the uncertainty in 1 − ΦF, but the tentative values of Δμ and Δα̅ indicated in Figure 5 are nevertheless obviously too large for a small

VI. CONCLUSIONS The fluorescence and SF spectroscopy investigations were performed for rubrene dispersed in a PMMA film. The contribution of the Stark shift of the fluorescence band was observed in the SF spectrum. The difference in the polarizability between the fluorescent state and the FC ground state was evaluated to be f 2 Δα̅ = 83 ± 6 Å3, where f is the internal field factor. This value is in good agreement with that obtained from the EA spectroscopy. In the SF spectrum, the decrease of the fluorescence quantum yield in an external electric field was also observed. A model for interpretation of electric field effects on the fluorescence quantum yield was presented. In the model, we consider that the Stark shift of the energy levels for the singlet and triplet states induces the change in the activation energy of the ISC process and the corresponding change in the 5502

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Article

The Journal of Physical Chemistry A

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ISC rate. In addition, we calculated the ensemble average of the change in the ISC rate over all orientations of the molecules, from which the expression of the fluorescence quenching was derived. Then the fluorescence quenching induced by the electric field was expressed in terms of the molecular parameters. By solving the equation, we obtained the tentative values of the molecular parameters, but they were physically unacceptable. To explain the observed magnitude of the fieldinduced quenching, we should take into account the effects of an external electric field on other nonradiative processes in addition to the ISC. Some useful experiments to confirm the change in the ISC rate and further gain insight into the mechanism of the effects of an external electric field on the photophysics of rubrene were argued.

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ASSOCIATED CONTENT

S Supporting Information *

Derivations of expressions used in the text. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b02627. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-143-465767. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partly supported by MEXT KAKENHI Grant No. 25870018. T.I. acknowledges CASIO science promotion foundation and the cooperative research program of Network Joint Research Center for Materials and Devices.

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REFERENCES

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DOI: 10.1021/acs.jpca.6b02627 J. Phys. Chem. A 2016, 120, 5497−5503